Pre Calculus Trigonometry in Right Angles

The most common use of trigonometry is in right triangles. There are formulas for the sine, cosine and tangent of the acute angle in a right triangle. The shortcut to remember these formulas is known as SOHCAHTOA, which is explained in detail in this lecture. If you're having trouble remembering the word SOHCAHTOA, there's a mnemonic that'll help you remember it more easily. You'll learn how to solve the right triangle using trigonometry. It is important to know that SOHCAHTOA only works in right triangles. For other triangles there are some other rules that can be used, which will be covered in the next lecture.

Can you use sin, cosin, or tangent in any order for angle theta or c to get the angle measurements? In other words, you used the tan of theta and the sin of c in the third example. Could I have used the tangent of theta and the cosign or tangent of c, instead of the sin of c?

2 answers

Last reply by: Dr. William MurrayTue Aug 5, 2014 11:50 AM

Post by Joshua Jacobon July 19, 2014

Sorry if this is a little unrelated but is it possible to do arcsin, arccos, and arctan on a graphing calculator? Is it the same thing as sin^-1...etc. Thank you for making these amazing lectures!

1 answer

Last reply by: Dr. William MurrayThu Jul 18, 2013 8:25 AM

Post by Manfred Bergeron July 7, 2013

Unless I'm missing anything crucial here, the fact that SOCAHTOA only works for right triangles stems directly from the basic definition of the the unit circle, which is essentially the pythagorian theorem.

1 answer

Last reply by: Dr. William MurrayMon May 6, 2013 8:54 PM

Post by Emily Engleon May 5, 2013

How would you solve for the inverse ratios without a calculator?

Trigonometry in Right Angles

Main formulas:

Master formula for right triangles: SOHCAHTOA!

sinθ =

oppositeside

hypotenuse

cosθ =

adjacentside

hypotenuse

tanθ =

oppositeside

adjacentside

Example 1:

A right triangle has short sides of length 3 and 4. Find all the angles in the triangle.

Example 2:

A right triangle has one angle measuring 40° and opposite side of length 6. Find the lengths of all the sides.

Example 3:

The lengths of the two short sides of a right triangle are in a 5:2 ratio. Find all angles of the triangle.

Example 4:

A right triangle has short sides of length 3 and hypotenuse of length 7. Find all the angles in the triangle.

Example 5:

A right triangle has one angle of 65° and hypotenuse of length 3. Find the lengths of all the sides of the triangle.

Trigonometry in Right Angles

Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture.

There's a very important step here that many students get confused about which is that, if you're looking for an answer in terms of degrees, which in real world measurement, it sometimes easier to use degrees than radians.0257

Remember that you want to have your calculator in degree mode here, because if you have your calculator in radian mode, you'll get an answer in radian which would look very different from any answer in degrees that you were expecting.0783

I calculate arctan(5/2), and it tells me that that is approximately equal to 68.2 degrees.0800